Yes, I'd imagine "more people come to the king with their problems" is the narrative reason for the Cent increase. But it still doesn't make much intuitive sense that building roads could destabilise and break our civilization.
It's tempting to just build them anyway and see what happens when Cent tops out as a result, but apparently we don't want to go there (I gather it's quite destructive).
Think of it as some mechanical system. We designed a sorting system for a factory that takes in gears and sorts them very precisely, checking for even minor defects. It has intake tubes/belts/etc leading to various gear factory buildings, each of which has its own smaller sorting system, its own connections between machines, and each of which produces a wide variety of gears. We've got really good intakes between the smaller sorting systems and the main one (Gravel roads between province capitals), but the interior ones are kinda old and rusted and outdated, and the smaller sorting systems vary in quality as well, so the actual throughput to the main sorting system is a lot lower than the theoretical; some of the intakes are jammed, others have holes that smaller gears just drop through, and some of the smaller sorting systems aren't programmed with the same priorities, and give false positives and/or negatives on defects, or not sending gears through to the main building that should. Still, the main sorting system does its job well, and while it takes longer than other models due to the precision, it's got more than enough time to handle the
actual throughput.
Then, the owner of the factory finally decides to replace a bunch of those intake feeds...and suddenly the actual throughput is way too much. Without smaller gears dropping through holes (marginal populace unable to make it to the king for appeals), and with all the conveyor belts working at full speed instead of some being slower (northern People deciding its too much effort to go to the king), and with the smaller sorting systems having more maintenance and finally sending what they should (greater possible oversight meaning provincial chiefs can't hide things from the king as easily), suddenly taking the time to separate gears by hundredths of an inch precision, and checking and repairing even the smallest dent or discoloration means the main sorting system is ridiculously overworked. It just isn't powerful enough to handle the actual throughput. So now the factory owner has a few choices:
-Buy a bigger, more expensive, and better central processing and sorting system (The Palace)
-Remove some of the intakes from the system (let provinces go)
-Improve the sub-building sorting systems and let them handle more things themselves instead of sending it to the main building (give the provinces more power)
-Lighten up the precision and defect checking (lower standards for catching corruption and whatnot)
-Try to power through and wait for a better model to be invented (Do nothing, stay on red centralization...though at least with us that would help inspire the innovation even if it would be painful)